Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 54 min ago
PreprintarXiv licencearXiv

Aspherical manifolds with nonvanishing tautological classes

  • Mauricio Bustamante
Open at sourcePDFDOICite

Abstract

For every even integer m≥ 2, we construct a closed, orientable, smooth, aspherical (2m+1)-manifold whose fundamental group has nontrivial center and for which infinitely many tautological classes in the 𝔽2-cohomology of the classifying space of its group of homotopically trivial diffeomorphisms are nonzero and not nilpotent. Specializing the calculation to cohomological degree $0$ gives examples of such manifolds that do not bound compact smooth manifolds. These provide counterexamples to a conjecture of Hebestreit--Land--Lück--Randal-Williams.

Related

  1. Tautological classes on KSBA spaces
    Valery Alexeev
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Hodge integrals on admissible covers and tautological projections of Prym classes
    Yoav Len, Sam Molcho, Navid Nabijou
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. On totally c-symplectically aspherical manifolds
    Luca F. Di Cerbo, Alexander Dranishnikov, Ekansh Jauhari
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv
  4. Exotic diffeomorphisms on closed aspherical $4$-manifolds
    Hokuto Konno, Jianfeng Lin, Anubhav Mukherjee +1
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. Aspherical Symplectic Manifolds with Positive First Chern Degree
    Jingcao Wu
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{bustamante2026aspherical,
  title = {{Aspherical manifolds with nonvanishing tautological classes}},
  author = {Mauricio Bustamante},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06345},
  eprint = {2609.06345},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06345},
}
RIS
TY  - UNPB
TI  - Aspherical manifolds with nonvanishing tautological classes
AU  - Mauricio Bustamante
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06345
UR  - https://arxiv.org/abs/2609.06345
AB  - For every even integer m≥ 2, we construct a closed, orientable, smooth, aspherical (2m+1)-manifold whose fundamental group has nontrivial center and for which infinitely many tautological classes in the 𝔽_2-cohomology of the classifying space of its group of homotopically trivial diffeomorphisms are nonzero and not nilpotent. Specializing the calculation to cohomological degree $0$ gives examples of such manifolds that do not bound compact smooth manifolds. These provide counterexamples to a conjecture of Hebestreit--Land--Lück--Randal-Williams.
ER  -